Complex Systems

Discovering Nontrivial and Functional Behavior in Register Machines Download PDF

Anthony Joseph
Past Student
University of Technology Sydney


Nontrivial and functional behavior in register machines is examined. Register machines are simple implementations of modern information and communications technology and provide a computationally simple vehicle for investigating examples of nontrivial and functional behavior. They also provide opportunities for optimizing information and communication technologies to use fewer resources or perform functions more quickly.

A simple two-register, four-instruction register machine was analyzed using soft and hard analytical techniques. Examples of nontrivial and functional behavior were identified by observing two-register, four-instruction register machines with various initial conditions. These register machines were identified by an exhaustive search of all possible register machine configurations meeting a particular definition. A subsequent investigation into the randomness in register machine components involved a frequency analysis, comparing program counter and register values against the discrete uniform distribution.

It is possible to observe examples of cyclical and conditional behavior, register-dependent and register-independent behavior, randomness in the register machine's program counter and registers, and foundation arithmetic functions. Further analysis of this register machine configuration yields opportunities for synthesizing multiple functions into a single register machine and optimizing functional register machines by brute-force testing all possible register machines.